A hard and brittle material means a brittle material with a high degree of hardness, and generally includes glasses, ceramics, stone materials, and semiconductor crystalline materials. Among hard and brittle materials, materials having a Vickers hardness of 1,500 Hv or higher, such as diamond, aluminum oxide (sapphire), silicon carbide, boron carbide, zirconium carbide, tungsten carbide, silicon nitride, titanium nitride, and gallium nitride, in general have a low reactivity due to their very high chemical stability, and also have a very high degree of hardness, and thus these materials are not readily-polishable. Therefore, these materials are usually finished through a diamond lapping process followed by polishing with colloidal silica to remove the scratches left by the lapping. In this case, however, a lengthy polishing is necessary to obtain a highly smooth surface.
Moreover, it has been known to polish sapphire substrates with a polishing composition containing a relatively high concentration of colloidal silica (see, for instance, Patent Document 1), and it has also been known to polish silicon carbide substrates with a polishing composition containing colloidal silica and having a specific pH (see, for instance, Patent Document 2). However, these cases have the problem that a sufficient polishing rate (removal rate) cannot be accomplished.